Question

what will be the slope of v(infinity)-vt vs t graph
1. log a
2 k/2.3030
3.-k/2.303
4 0​

Answer 1

Given :

Graph of  $V_{\alpha }$ - $V_{t}$ vs t

To Find:

Slope of  $V_{\alpha }$- $V_{t}$ vs t graph

Explanation:

t=time

k=rate constant

$V_{\alpha }$=Volume at infinite time

$V_{t}$ = Volume at time - t

V₀ = Initial  Volume

The equation for time in terms of other variables is given by :

$t=\frac{1}{k} (ln(\frac{V_{\alpha }-V_{0} }{V_{\alpha }-V_{t} } ))$

$kt=ln(V_{\alpha } -V_{0} )-ln(V_{\alpha } -V_{t} )$

$ln(V_{\alpha } -V_{t} )=-kt + ln(V_{\alpha } -V_{0} )$

$2.303 log ( V_{\alpha } -V_{t} )=-kt + 2.303 log (V_{\alpha } -V_{0} )$

$log ( V_{\alpha } -V_{t} )=-k\frac{t}{2.303} + log (V_{\alpha } -V_{0} )$

Comparing with

$y=mx+c$

We have,

m = slope = $-k\frac{t}{2.303}$

So, the final answer will be Option 3.